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We investigate a plasmon-induced transparency (PIT)-like behavior at terahertz (THz) region induced by resonance detuning in a hybrid planar metamaterial (MM). Each unit cell of the MM contains two types of dipole oscillation resonators: a cut-wire and a couple of U-shaped resonators in mirror symmetry. The hybridization of above resonators splits the single resonance mode into two side modes in THz transmission spectrum. The side modes are found to induce negative group delays of incident THz wave-packet. The distribution of surface currents and electric energy reveals that the near-field coupling between cut-wire and U-shape resonators results in inductive-capacitive (LC) resonance, which dominates the low frequency side mode, while the high frequency side mode attribute to the triple dipole oscillations. The reduction of the length of cut-wire give rise to a dipole resonance detuning, which enhances the LC resonance via near-field coupling, while attenuates the constructive inference of triple dipole oscillators. The retrieved complex dielectric functions indicate the evolution of LC resonance and triple dipole oscillations. By controlling the dipole resonance detuning appropriately, a man-made transparent tip can be created in between the two side modes. However, such a transparent tip is unable to induce negative group delay. Aforementioned PIT-like behavior can support the design of hybrid planar MMs in application of two-band notch filters or multi-channel buffer in the THz-region.
© 2016 Optical Society of America
1. Introduction
A plasmonic analogue of electromagnetically induced transparency (PIT) effect is naturally a destructive interference between two different modes being excited simultaneously with different coupling strengths [1–3]. Such an effect leads to mimick cost-effectively the electromagnetically-induced transparency phenomenon from optical frequency to terahertz (THz) region [4–9]. PIT effect can be achieved in a variety of basic electromagnetic resonators of metamaterials (MMs), such as split-ring resonators (SRR) [4–6], cut-wires [7,8], and U-shape resonators [9,10]. To achieve PIT effect, it is required that the mode-frequencies of two basic resonators are nearly identical but with significantly different quality factors (Q factors), namely a narrow high-Q mode and a broad low-Q mode [1–10]. The PIT spectral configuration can be tuned either by controlling the coupling strength between high-Q mode and low-Q mode [9–11]. These works have been focused on the optimization of the narrow transparency tip of PIT effect to slow down the light speeds. The rapid development of bidirectional data transfer in THz-based telecommunication systems require a multi-channel filter designed for THz wavelength division multiplexing [12–15]. To a hybrid planar MM, the occurrence of transparency tip results in two adjacent absorption tips in transmission spectrum, termed as side modes. As such, the hybrid planar MMs could be potential two band filters for the application of multi-channel THz communication as long as above side modes are tuned appropriately [16,17].
In this work, we demonstrate a PIT-like behavior in hybrid planar MMs, which are fabricated following the requirement of PIT-effect. Such a hybrid planar MM composed of a cut-wire and a couple of U-shaped resonators in mirror symmetry. A length reduction of cut-wire results in a frequency detuning, which gives arise to a PIT-like behavior. The evolution of side modes is evaluated using THz time-domain spectroscopy (THz-TDS). The origin of PIT-like behavior is revealed by mapping the electric field and the THz-induced surface current in the hybrid planar MMs.
2. Experiment
The MMs are prepared via a conventional micro-fabrication process. The resonators patterns are transferred onto 625 μm-thick semi-insulating gallium arsenide (SI-GaAs) substrates by photolithography. A metal layer of 120 nm thick gold (Au) and 5 nm thick titanium (Ti) is deposited on the patterned substrate. The Ti acts as an adhesion layer between Au and SI-GaAs. The lattice period of MM is 60 μm. The detailed structures of our hybrid planar MMs are presented in Fig. 1(a). Such a MM consists of two independent resonators: The first basic resonator is a cut-wire of 48 μm length and 4 μm width. The second one is a couple of U-shaped resonators in mirror symmetry, which has 40 μm long baselines and 14 μm short arms. The widths of U-shaped resonators are identical to 4 μm. Then, the cut-wire is inserted into the middle line of U-shaped resonators along the X-axis, the proposed PIT-like MM is achieved. Here, we select 4 MM samples with different length of cut-wires (48 μm, 40 μm, 32 μm, and 28 μm) to study the evolution of PIT-like behavior, respectively. The THz radiation is normally incident on the surface of the samples, as shown in Fig. 1(b). In this configuration, the electric component is parallel to the length of the cut-wire as shown in Fig. 1(c). Then, only dipole resonance mode can be observed when the electric field of incident THz radiation is parallel to the cut-wire [18,19]. As such, the case of THz polarization perpendicular to the cut-wire is ignored in our work. The transmission spectra of the samples were measured by a commercial THz-TDS system (TERA K15, Menlosystem). The detected THz signals are read out into an integrated Lock-In amplifier at the time constant of 100 ms. The resonance modes are recorded in the frequency range from 0.3 THz to 2.0 THz. All THz measurements are conducted in nitrogen atmosphere so as to avoid water absorption in air. A bare SI-GaAs wafer identical to the sample substrate served as a reference. The THz radiation is in normal incidence onto the metal layer of MMs. The transmission spectrum is extracted from Fourier transforms of the measured time-domain electric fields, which is defined as [18]:
where Esample(ν) and Eref(ν) are the Fourier transformed electric fields through the sample and reference, respectively. T(ν) is the transmittance as a function of THz frequency. Finally, a finite difference time domain (FDTD) algorithm based commercial software CST Microwave StudioTM was used to simulate the THz transmittance as well as to map the surface currents and electric energy density distribution.
Fig. 1 (a) Schematic diagram of the unit cell, in which a = 60 μm, l = 40 μm, g = 4 μm, w = 4 μm, s = 14 μm, h = 625 μm, L = 48 μm, respectively. Here, the characters of i, ii, iii, and iv refer to the unit cells of cut-wires with different length of 48, 40, 32, 28 μm correspondingly. (b) Experimental illustration of the THz-TDS measurement of the MMs. (c) The polarization of incident THz pulse and XYZ-coordination.
3. Results and discussion
The THz transmittances of the basic resonators are shown in Fig. 2, which are derived from the fast Fourier transform of the measured THz time domain data. The Q factors of resonance modes are calculated as below [19]:
where ν is the mode frequency and Δν is the mode linewidth. Correspondingly, the details of resonance modes are listed in Table 1.Fig. 2 THz transmittance of (a) cut-wire and of (b) U-shaped resonators, respectively. Blue solid-line refers to the measured THz transmittance. Red solid-line refers to the simulated THz transmittance. The electric density at resonance modes of (c) cut-wire and of (d) U-shaped resonators, respectively. The surface current distribution at resonance mode of (e) cut-wire and of (f) U-shaped resonators, respectively.
Table 1. Resonance modes of basic resonators
In order to achieve an optimal simulation data, the permittivity of SI-GaAs substrate (ε = 13.2) is measured by THz-TDS since the resonance mode is subject to the dielectric environment of substate [20]. Owing to the limitation of the patterning accuracy in photolithography-based fabrication process, there is inevitable imperfection at edge of each unit cells, which leads to the THz scattering [21]. The intrinsic defects of SI-GaAs and above scattering process occur, which results in slight deviations between the measurement and the simulation. The central frequencies of both resonators are at around 1.08 THz, while the resonance linewidth of U-shaped resonators is twice to the mode of cut-wire. Therefore, the U-shaped resonators contribute to the low-Q mode, and the cut-wire serves as high-Q mode resonator. The electric energy distributions of high-Q and low-Q modes are shown in Fig. 2(c)-2(d), both of which are accumulating at the terminals of the metal structures. To the U-shaped resonator, there is no obvious energy localization at the gap area, which differs from the SRR. The origin of modes can be realized via surface current analysis. As shown in Fig. 2(e)-2(f), the mono-directional surface currents indicate that the dipole oscillations dominate the resonance mode of cut-wire [2,19], and a couple of parallel current flows along the up-and-down baselines of the U-shape resonators. Unlike the SRR, there is no circulating current in the U-shape resonators. At this point, the low-Q mode of U-shape resonators attributes to a coupled dipole oscillations.
Since the cut-wire and U-shaped resonators have the same resonance frequency but the different Q factors of resonance modes, a PIT-effect can be achieved from the combination of above two types of basic resonators. Figure 3(a) displays a schematic illustration of the unit cell of hybrid planar MM, which consists of a metallic cut-wire symmetrically placed on the center of a couple of U-shaped resonators. The length of the cut-wire shrinks with respect to the horizontal symmetry axis of the U-shaped resonator. Figure 3(b)-3(c) shows the measured and simulated THz transmittance of hybird MMs. Conventionally, a transparent tip should occurs at the resonance mode of basic resonators (1.08 THz) [1–18]. To our surprise, however, the foreseen transparent tip disappears at above frequency in our hybrid planar MMs. Alternatively, the original resonance mode splits into two side modes in transmission spectrum. One is below 1.08 THz, while the other is above 1.08 THz. Herein, we define that the low frequency side modes as νL, while the high frequency side modes as νH, respectively. As shown in Fig. 3, both νL and νH exhibit a slight blueshift trend in the frequency spectra when the length of cut-wire reduces. Simultaneously, the transmittance of νL rises up while that of νH gets down when the cut-wire shrinks. Such a behavior is not the same as regular PIT-effect, but seems to be much more like a teeter-totter effect in C-shaped complementary split-ring resonators [22]. The accurate positions of above two side modes are listed in Table 2.
Fig. 3 (a) Illustration of hybrid planar MMs, which are in combination of cut-wire and U-shaped resonators. (b) THz transmittance of above MMs. (b) The measured THz transmittance. (c) The simulated THz transmittance, respectively.
Table 2. Properties of νL and νH of MMs with different lengths of cut-wiresa
When the length of cut-wire is set in the range between 40 μm and 32 μm, the transparent tips νT occurs in the transmittance spectrum. Such transparent tips seem to be like crossover points formed by the absorption tails of νL and νH modes. Meanwhile, the resonance linewidth of νL increases, while that of νH decreases. This rises up the Q factor of νL mode and pull down the Q factor of νH mode, respectively. Above phenomenon is totally different from the destructive inference of the modes of basic resonators. At this point, it could be recognized as a PIT-like behavior.
The significant evidence of PIT effect is a negative group delay (Δtg) at the transparent tips in frequency spectrum [5,18]. Here, the Δtg represent the time delay of THz wave packet instead of the group index. The Δtg can be calculated from the equation as below [5]:
where φ and ν refer to the effective phase and frequency of THz complex transmission spectrum, respectively. To determine the φ, the phase of incident THz wave is subtracted, traveling in the free-space between input port and the metasurface, from the phase between the input and out port. As such, only the desired phase difference between free-space and the output port which is positioned 625 μm behind the MMs. From the measured spectra, however, the phase of free-space is initially subtracted from the measured phase of MMs. An additional phase delay of free-space with the thickness of 625 μm was manually added to the subtraction. Such a calculation method is the same as the retrieval of the group delay of PIT phenomenon of double split-ring resonators based MMs [5].Figure 4(a) shows the experimental measured phase spectrum of our MMs, in which a distinct phase transition is found at the νL and νH modes. Following aforementioned retrieval method of group delay, a negative group delay occurs at the frequencies of two side modes, which is shown in Fig. 4(b). At νL mode, the Δtg decreases monotonically from −8 ps to −45 ps when the length of cut-wire reduces from 48 μm to 28 μm. At νH mode, however, the Δtg increase from −35 ps to 0 ps correspondingly. In our case, the transparent tip νT appears when the cut-wire is set at 40 μm and 32 μm, however, there is no evidently negative group delay at this transparent tip. As such, the THz response of our hybrid planar MMs is recognized not as a regular PIT-effect but as a PIT-like behavior. The transparency-like point νT locates in between the νL and νH modes and there is no group delay effect at this position. As such, we propose that the νT maybe the cross-point of the spectral tailors of the νL and νH modes.
In order to reveal the evolution of above PIT-like behavior, the complex permittivity as a function of THz frequency needs to be calculated as below [23]:
The permittivity can be derived from the parameters of S11 and S21 calculated by CST Microwave StudioTM software. Initially, one can achieve the effective refractive index n and impedance z following the equation below [23]: Here, the permittivity ε is directly calculated from ε = n/z.Figure 5 shows the retrieved complex permittivity of the hybrid MM with the length of cut-wire of 48 μm, 40 μm, 32 μm, and 28 μm, respectively. To the modes of νL and νH, the real part of the function of complex permittivity ε’ shows a large negative value, while the imaginary part ε” shows large positive values, describing a lossy medium at these frequencies. Since the dielectric function is flat the frequency of νT modes, it is an evidence that the νT is induced by the spectral tailors crossing of the νL and νH modes. Comparing the Fig. 3 and the Fig. 5, it is evident that a dramatic variation of negative ε’ corresponds to a strong side mode oscillation accompanied by a large positive ε”. According to the principle of frequency selective surface, both the electric dipole oscillation and the inductive-capacitive (LC) resonance can induce the negative ε’ in MMs [22,24]. However, above two possible origins have totally different performances on THz-induced surface currents.
Fig. 5 The frequency-dependent dielectric functions of hybrid MMs. The blue curves refers to the real permittivity ε'. The red lines refer to the imaginary permittivity ε”.
The current distributions of νL mode and of νH mode are shown in Fig. 6. In our case, the cut-wire is the symmetric axis of the unit cell. The surface current distribution and direction is seen as mirror images between the upper and lower halves of the unit cell. To the νL modes, it is obvious that anti-parallel currents are produced in baseline of U-shaped resonators and cut-wire. Then, a couple of circulating surface currents occur in the upper and lower halves of the unit cell. Since the circulating current is the evidence of the LC resonance, we proposed that the two localized LC resonance give arise to the low frequency mode νL. The intensity of surface current indicates that U-shaped resonators experience a strong coupling to incident THz radiation owing to the length reduction of cut-wire. In accordance with the Ampère's right hand screw rules [25], the direction of circulating surface current is counter-clockwise in the upper half unit cell, which induces a magnetic flux along the direction of incident THz wave-vector. In lower half unit cell, the direction of circulating surface current becomes clockwise. It induces a magnetic flux opposite to the direction of THz wave-vector. The magnetic field interacts with resonators to produce an electromotive force. As such, the surface currents-induced magnetic flux produces another current whose magnetic field opposes the change which produces it. Since the opposing currents will repel each other, it is the evident that the strength of surface current decreases on the cut-wire but increases on the baseline of the U-shape resonators. The length reduction of cut-wire enhances aforementioned electromagnetic induction effect. For the high frequency modes νH, however, the surface current flows are all parallel on the cut-wire as well as on the baseline of U-shaped resonators. It is an evidence of triple dipole oscillators. Regarding the structural symmetry of the unit cell, only dipolar resonance in nature is excited due to the constructive interference of charge oscillation in resonators, which is able to strongly couple with the incident THz wave [26]. Here, we address that the quadrupole oscillation can be excluded from the origin of the νH modes since it needs an asymmetric geometry [27]. As shown in Fig. 6, the triple dipoles oscillating constructively in phase and amplitude, which causes a coupled dipolar resonance at νH modes. However, a length reduction of cut-wire shifts one of the dipole oscillations to a higher frequency. The mode frequency of dipole oscillation is subject to the length of cut-wire. The mode frequency of independent cut-wire with different lengths are simulated.
Fig. 6 Surface currents of hybrid MMs: (i), (ii), (iii) and (iv) refers to the length of cut-wire L = 48, 40, 32, 28 μm correspondingly. The νL and νH refers to the low-frequency mode and high frequency mode respectively. The symbols of out-of-plane axial vector refer to the magnetic field. The arrows indicate surface current direction. The color bar refers to the relative strength of surface currents.
Figure 7 shows the simulated THz transmittance of cut-wires with the length of 48 μm, 40 μm, 34 μm, and 28 μm, respectively. Here, the polarization of the incident THz electric field is parallel to the cut-wire and the propagation direction is normal to the plane of the unit cell. Such a frequency detuning attenuates constructive interference of triple dipole oscillations so as to weaken the strength of νH modes.
Fig. 7 The simulated THz transmittance of cut-wires with different lengths. The polarization of the incident THz electric field is parallel to the gap. The black solid-line, red solid-line, blue-solid line, and purple solid line refer to the cut-wire with different length of 48 μm, 40 μm, 34 μm, and 28 μm, respectively.
The evolution of νL and νH modes can also be extracted from mapping the electric energy density distribution of unit cell, as shown in Fig. 8. To the νL modes, the electric energy concentrates at the gap between the terminals of U-shape resonators and cut-wire. To the νH modes, however, the electric energy distribute at the outer-edge of the above two types of metal structures, similar to the Fig. 2. When the length of cut-wire reduces, the electrical energy of νL modes gradually accumulate in the gap area between the terminals of U-shape resonators and cut-wire. In contrast, the electrical energy density of νH modes gradually diminishes. These results are in good agreement with the observed THz transmittance variation between the νL and νH modes, as shown in Fig. 3. The length reduction of cut-wire increases the near-field coupling strength between the cut-wire and U-shaped resonators. An intense energy accumulation in the gap area enhances the LC resonance, as shown in Fig. 8. However, such a length reduction breaks the constructive inference of triple dipole oscillators between the cut-wire and U-shaped resonators. As such, the contribution of U-shaped resonators become weaker gradually, and only the cut-wire in the middle of unit cell will be responsible for the dipole oscillation of νH modes.
Fig. 8 Electric density distribution of hybrid MMs: (i), (ii), (iii) and (iv) refer to the length of cut-wire L = 48, 40, 32, 28 μm correspondingly. The νL and νH refers to the low-frequency mode and high frequency mode respectively. The color bar refers to the relative strength of electric density.
4. Conclusion
In summary, an evolution of PIT-like behavior in hybrid planar MMs is investigated experimentally at THz region. Such a MM is composed of a cut-wire and a pair of U-shaped resonators in mirror symmetry. Both structures manifest dipole oscillation of the same resonant frequencies when being excited by the incident THz radiation. When they are combined into one unit cell, a mode split occurs. When the length of cut-wire decreases from 48 μm to 28 μm, the strength of low frequency modes increase, while the strength of the high frequency modes decrease monotonically. When the cut-wire’s length achieves 40 μm and 32 μm, a transparent tip emerges, which is shift away from the modes of basic resonators. Furthermore, a group delay is observed at the frequencies of side modes instead of the transparent tip. Therefore, it is recognized not as regular PIT-effect but a PIT-like behavior. The complex permittivity of MM is retrieved that a real part showing a large negative value, while the imaginary part shows large positive values at both side modes. The simulation of THz-induced surface current indicates that the inductive-capacitive (LC) resonance dominates the low frequency mode while the dipole oscillation dominates the high frequency mode. By tuning the length of the cut-wire, one can achieve a manmade transparent tip in between the two side modes. Such a PIT-like behavior suggests that our MMs have a potential as two-band notch filters or multi-channel buffer for THz telecommunication applications.
Acknowledgements
This work was financially supported by the National Natural Science Foundation of China (Grant No. 61307130) as well as the Innovation Program of Shanghai Municipal Education Commission (Grant No.14YZ077). ZZ acknowledges the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. WP acknowledges the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB04030000).
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